Synchronization for low-energy long-range communications

ABSTRACT

A receiver configured to receive a frequency-modulated transmission having a preamble and a corresponding method are provided, the receiver having a buffer coupled to an input terminal for receiving the transmission, a time-to-frequency transformer coupled to the buffer, an energy aggregator coupled to the transformer, a preamble detector coupled to the aggregator, and a symbol synchronizer coupled to the detector; the method including receiving a sequence of time-domain frequency-modulated samples, transforming the sequence of time-domain samples into a spectrum of frequency-domain data, and matching an actual energy distribution over a plurality of discrete frequencies in the frequency-domain data with an expected energy distribution of the preamble to determine frequency error.

TECHNICAL FIELD

Embodiments of the present inventive concept relate to communications,and more particularly, to a system and method for carrier frequencyerror determination and symbol synchronization in low-energy long-rangecommunications.

DISCUSSION OF RELATED ART

Wireless communications generally require synchronization at a receiverfor accurate decoding. Traditionally, a frame type of synchronizationhas been achieved via bit correlation after frequency demodulation.

SUMMARY

An exemplary embodiment method is provided for receiver symbolsynchronization in a frequency-modulated transmission having a preamble,and includes receiving a sequence of time-domain frequency-modulatedsamples, transforming the sequence of time-domain samples into aspectrum of frequency-domain data, and matching an actual energydistribution over a plurality of discrete frequencies in thefrequency-domain data with an expected energy distribution of thepreamble to determine frequency error.

The method may include comparing phase relationships at the plurality ofdiscrete frequencies to determine symbol timing. The method may beapplied where matching the expected energy distribution includescombining energies over the plurality of discrete frequencies.

The method may include receiving periodic samples of thefrequency-modulated transmission, buffering a plurality of the receivedsamples, performing a block transformation on the plurality of bufferedsamples into a plurality of frequency bins, comparing combined energiesfor each of a plurality of subsets of the plurality of frequency bins,each subset corresponding to the relative frequency distribution ofenergy expected in the preamble, selecting the subset with the greatestcombined energy to determine the carrier frequency error of thetransmission, and synchronizing receipt of the frequency-modulatedtransmission in accordance with the selected subset. The method mayinclude comparing the combined energies to a threshold, wherein if thethreshold is not exceeded receiving the next periodic samples, orwherein if the threshold is exceeded synchronizing the transmission anddetermining a fine carrier frequency error.

The method may include determining fractional symbol timing based onrelative frequency bin phases. The method may be applied where the blocktransformation is an n-point time-domain to frequency-domain transform,and fractional symbol timing is determined in accordance with relativefrequency bin phases of first and second bins separated by n/2 bins fordetermining high-precision symbol timing with an ambiguity, a third binseparated from the first bin by n/8 bins and a fourth bin separated fromthe second bin by n/8 bins for resolving the ambiguity.

The method may be applied where the block transformation is a 64-pointFast Fourier Transform (FFT). The method may include achieving symboltiming synchronization, and beginning demodulation of a main packetbased on the achieved synchronization.

The method may include comparing the subset with the greatest combinedenergy to a threshold, and if the combined energy exceeds the thresholdusing frequency bin phases to extract symbol timing. The method may beapplied where the frequency-modulated transmission is a Bluetooth™Low-Energy Long-Range transmission, and the preamble includes ten 8 μsas repetitions of the 8-bit pattern 00111100.

The method may be applied where the carrier frequency error is based ona fractional bin spacing. The method may include performing an alternateFFT with a ½ bin frequency offset to obtain a carrier frequency errorwithin ¼ bin.

An exemplary embodiment receiver is provided as configured to receive afrequency-modulated transmission having a preamble, the receiverincluding a buffer coupled to an input terminal for receiving thetransmission, a time-to-frequency transformer coupled to the buffer, anenergy aggregator coupled to the transformer, a preamble detectorcoupled to the aggregator, and a symbol synchronizer coupled to thedetector.

The receiver may include a start-pattern de-mapper coupled to thesynchronizer. The receiver may be configured as an I/Q receiver. Thereceiver may be configured as a direct conversion receiver, asuper-heterodyne receiver, or the like.

The receiver may be applied where the time-to-frequency transformer isan n-point Fast Fourier Transform (FFT) unit. The receiver may beapplied where the detector is configured to take squares of absolutevalues of transformed frequency bins, test summations of candidate binsets, and compare to a threshold.

The receiver may include an amplifier configured to receive an inputsignal, an analog-to-digital converter (ADC) connected to the amplifier,and a filter connected to the ADC, where the down-sampler is connectedto the filter, and the buffer is connected to the down-sampler andconfigured for receiving each sample to simultaneously hold a pluralityof data samples so a time-domain to frequency-domain transform may beperiodically performed on the data within the buffer.

The receiver may be applied where the down-sampler is configured todown-samples to symbol rate. The receiver may be applied where thebuffer is a first-in, first-out (FIFO) buffer.

The receiver may include a low-noise amplifier (LNA) configured toreceive an input signal, an oscillator configured to generate a cosinewave and a 90-degree offset sine wave, a first mixer connected to theLNA and the oscillator and configured to mix the input with the cosinewave to expose an in-phase (I) portion of the input signal, a secondmixer connected to the LNA and the oscillator and configured to mix theinput with the sine wave to expose a quadrature-phase (Q) portion of theinput signal, a first analog-to-digital converter (ADC) connected to thefirst mixer, a second ADC connected to the second mixer, a firstlow-pass filter (LPF) connected to the first ADC, a second LPF connectedto the second ADC, a first down-sampler connected to the first LPF andconfigured for down-sampling the in-phase I data, a second down-samplerconnected to the second LPF and configured for down-sampling thequadrature-phase Q data, and at least one buffer connected to thedown-samplers and configured for receiving each I/Q sample pair tosimultaneously hold a plurality of I/Q data sample pairs so atime-domain to frequency-domain transform may be performed on the datawithin this buffer periodically.

An exemplary embodiment program storage device is provided tangiblyembodying a program of instructions executable by a processor forreceiver symbol synchronization in a frequency-modulated transmissionhaving a preamble, the instructions including receiving a sequence oftime-domain frequency-modulated samples, transforming the sequence oftime-domain samples into a spectrum of frequency-domain data, andmatching an actual energy distribution over a plurality of discretefrequencies in the frequency-domain data with an expected energydistribution of the preamble to determine frequency error.

The instruction steps may include comparing phase relationships at theplurality of discrete frequencies to determine symbol timing. Theinstruction steps may be applied where matching the expected energydistribution includes combining energies over the plurality of discretefrequencies.

The instruction steps may include receiving periodic samples of thefrequency-modulated transmission, buffering a plurality of the receivedsamples, performing a block transformation on the plurality of bufferedsamples into a plurality of frequency bins, comparing combined energiesfor each of a plurality of subsets of the plurality of frequency bins,each subset corresponding to the relative frequency distribution ofenergy expected in the preamble, selecting the subset with the greatestcombined energy to determine the carrier frequency error of thetransmission, and synchronizing receipt of the frequency-modulatedtransmission in accordance with the selected subset. The instructionsteps may include comparing the combined energies to a threshold,wherein if the threshold is not exceeded receiving the next periodicsamples, or wherein if the threshold is exceeded synchronizing thetransmission and determining a fine carrier frequency error.

The instruction steps may include determining fractional symbol timingbased on relative frequency bin phases. The instruction steps may beapplied where the block transformation is an n-point time-domain tofrequency-domain transform, and fractional symbol timing is determinedin accordance with relative frequency bin phases of first and secondbins separated by n/2 bins for determining high-precision symbol timingwith an ambiguity, a third bin separated from the first bin by n/8 binsand a fourth bin separated from the second bin by n/8 bins for resolvingthe ambiguity.

The instruction steps may be applied where the block transformation is a64-point Fast Fourier Transform (FFT). The instruction steps may includeachieving symbol timing synchronization, and beginning demodulation of amain packet based on the achieved synchronization.

The instruction steps may include comparing the subset with the greatestcombined energy to a threshold, and if the combined energy exceeds thethreshold using frequency bin phases to extract symbol timing. Theinstruction steps may be applied where the frequency-modulatedtransmission is a Bluetooth™ Low-Energy Long-Range transmission, and thepreamble includes ten 8 μs repetitions of the 8-bit pattern 00111100.

The instruction steps may be applied where the carrier frequency erroris based on a fractional bin spacing. The instruction steps may includeperforming an alternate FFT with a% bin frequency offset to obtain acarrier frequency error within ¼ bin.

BRIEF DESCRIPTION OF THE DRAWINGS

Aspects of the present inventive concept may become apparent andappreciated upon consideration of the following description of exemplaryembodiments when taken in conjunction with the accompanying drawings, inwhich:

FIG. 1 is a schematic block diagram of an I/Q receiver in accordancewith an exemplary embodiment of the present inventive concept;

FIG. 2 is a schematic block diagram of an I/Q receiver with FFT detectorin accordance with an exemplary embodiment of the present inventiveconcept;

FIG. 3 is a graphical diagram comparing coherent and incoherentsummation of a spoof signal received by an I/Q receiver with FFTdetector in accordance with an exemplary embodiment of the presentinventive concept;

FIG. 4 is a graphical diagram of FFT bins for the spoof signal receivedby an I/Q receiver with FFT detector in accordance with an exemplaryembodiment of the present inventive concept;

FIG. 5 is a graphical diagram comparing coherent and incoherentsummation of FFT bins for a signal received by an I/Q receiver with FFTdetector in accordance with an exemplary embodiment of the presentinventive concept; and

FIG. 6 is a schematic flow diagram for a method of operating an I/Qreceiver with FFT detector in accordance with an exemplary embodiment ofthe present inventive concept.

DETAILED DESCRIPTION

Bluetooth™ Low-Energy (BLE) Long-Range is a wireless communicationsprotocol expected to operate at low Signal-to-Noise Ratios (SNR) such asaround zero decibels (dB). Using an 8 μs repetition period, the BLELong-Range preamble includes 10 repetitions of the 8-bit pattern00111100. Various methodologies for determining carrier frequency errorand achieving symbol synchronization are possible. Here, a coarsecarrier frequency error may be determined through finding the locationof a best matching frequency bin pattern prior to thresholding andsynchronization, while a fine carrier frequency error may be determinedthrough thresholding and synchronization.

Symbol synchronization (Sync) may be approached by a correlation of thereceived signal with an ideal realization of the signal. Thiscorrelation could be performed in the Cartesian-domain or in thefrequency-domain for each candidate Sync position. A correlation ofsufficient magnitude would indicate Sync, and at the maximum correlationvalue provide symbol timing.

A Cartesian-domain correlation has excellent performance at low SNR, butthe complexity of the correlator increases as n² so it quickly becomesan expensive solution for long sequences. Cartesian correlation isdesensitized by frequency errors, which may necessitate the use of amatched filter bank to consider multiple frequency offset candidatesthereby adding to the complexity.

A frequency-domain correlation, which may involve a phasedifferentiation (e.g., FM demodulation) of the received I/Q data andcomparison against the expected bit pattern, is efficient at high SNRand robust to frequency error. It has been used for standard Bluetooth™(BT) and Bluetooth™ Low-Energy (BLE). Like Cartesian-domain correlation,its complexity rises as n². It is less effective at low SNR as there issignificant loss of SNR in the I/Q to frequency-domain conversion whenthe operating SNR is low.

In Orthogonal Frequency-Division Multiplexing (OFDM) such as IEEE 802.11OFDM PHY, the preamble has a frequency structure resulting intime-domain repetition. As with OFDM modulation, Fast Fourier Transform(FFT) methods may be used to achieve time/frequency synchronization inBLE Long-Range. However, the preamble frequency structure such as tonespacing and tone power for BLE Long-Range is quite different.

As shown in FIG. 1, an exemplary embodiment I/Q receiver is indicatedgenerally by the reference numeral 100. The I/Q receiver 100 includes alow-noise amplifier (LNA) 110 configured to receive an input signal, anoscillator 111 configured to generate a cosine wave and a 90-degreeoffset sine wave, a first mixer 112 connected to the LNA and theoscillator and configured to mix the input with the cosine wave toexpose the in-phase (I) portion of the input signal, a second mixer 113connected to the LNA and the oscillator and configured to mix the inputwith the sine wave to expose the quadrature-phase (Q) portion of theinput signal, a first analog-to-digital converter (ADC) 114 connected tothe first mixer, a second ADC 115 connected to the second mixer, a firstlow-pass filter (LPF) 116 connected to the first ADC, a second LPF 117connected to the second ADC, a first down-sampler 118 connected to thefirst LPF and configured for down-sampling the in-phase I data to 1 MHz,a second down-sampler 119 connected to the second LPF and configured fordown-sampling the quadrature-phase Q data to 1 MHz, and buffer 120, suchas a first-in first-out (FIFO) buffer, connected to the down-samplersand configured for receiving each I/Q sample pair to simultaneously hold64 I/Q data sample pairs so an FFT may be performed on the data withinthis buffer at least every 8 μs.

The exemplary embodiment receiver 100 uses a direct conversion receiverarchitecture capable of implementing the inventive concept, although theinventive concept is not limited to this type of architecture. Forexample, a super-heterodyne type of receiver or the like may be used inalternate embodiments. At the LNA 110, the signal is received in the2.4-2.48 GHz Industrial, Scientific and Medical (ISM) band, which isnext amplified, mixed, and sampled. The signal is then digitized and atleast low-pass filtered using a filter having sufficiently widebandwidth, here 1.3 MHz, to allow passage of the BLE Long Range signalincluding any frequency offset prior to down-sampling. Thus, theinventive concept works on the buffered I/Q data, down-sampled in thisexemplary embodiment to 1 million samples per second (MSample/s).

Turning to FIG. 2, an exemplary embodiment I/Q receiver is indicatedgenerally by the reference numeral 200. The I/Q receiver 200 is similarto the I/Q receiver 100 of FIG. 1, so duplicate description may beomitted. In addition, the I/Q receiver 200 includes a 64-point FFT unit130 connected to the buffer 120. The buffer 120 may be a FIFO bufferwith serial access, and/or support simultaneous parallel access to allof its 64 I/Q sample stores. The receiver 200 further includes adetector 140 configured to take absolute (ABS) values (and/or squares)of the FFT bins, test summations (Z) of candidate 4-bin (oralternatively 6-bin) sets, and compare to a threshold. The detector, inturn, is connected to a synchronizer 150. If the threshold is notexceeded, the detector signals the FFT device 130 and awaits the nextFFT; but when the threshold is exceeded, the detector passes a Syncsignal to the synchronizer 150. Upon receipt of the Sync signal, thesynchronizer 150 enters a Sync-achieved state, where the 4 (oralternatively 6) bin set with the largest summation is used to determinethe frequency error, and the bin phases are used to determine symboltiming. A start-pattern de-mapper 160 is connected to the synchronizer,in turn, and configured to de-map the synchronized start-pattern data.

Turning now to FIG. 3, a graphical comparison of coherent (e.g.,in-phase) and incoherent/non-coherent (e.g., out-of-phase) summation fora spoof signal received by an exemplary I/Q receiver, such as the I/Qreceiver 200 of FIG. 2, is indicated generally by the reference numeral300. Here, the coherent summation 310 has significantly lower continuousand peak correlated magnitude output than the incoherent summation 320.

When summing the result vectors of successive FFT frames together, onecan just add the magnitudes, which is an incoherent sum, or sum thecomplex vectors, which is a coherent sum. With the coherent combination,any stationary sinusoids with a frequency mid-way between 2 FFT binsacross 2 successive FFT frames, for example, would cancel out instead ofsumming in spectrum. Here, the significantly lower peak magnitude of thecoherent summation 310 indicates that the frequency bins are not inperfect phase. Here, coherent indicates that a phase relationship isenforced on the bins. Thus, if the complex vectors are summed, all ofthe phases must be equal to get the maximum sum. The phase relationshipof the bins changes depending on the starting point of the FFT, and onlyfor one point will all the phases be equal. However, the spoofing signalchosen has a phase relationship that would never exist for a realsignal, but all phase information is neglected by taking the absolutevalue or squaring.

Use of the inventive concept may be detected by sending such a spoofsignal before the main waveform or normal packet in a throughput test. Aproduct deploying the inventive concept would Sync on such anamplitude-modulated (AM) spoof signal but then fail to decode the accesscode and packet. The result should be a detectable loss in throughput. Amethod not employing the inventive concept should not Sync to thespoofing signal and thus have no loss in throughput versus its standardperformance. Although this spoof signal is for six (6) bins, details ofhow many bins such as four (4), and which bins are used such as theinner four, and how the bins are summed such as sum of squares orabsolute values, may lead to different optimal spoof signals inalternate embodiments.

As shown in FIG. 4, a graphical representation of normalized magnitudesfor all 6 FFT bins of a real BLE long range signal received by anexemplary I/Q receiver like that of FIG. 2 is indicated generally by thereference numeral 400. The normalized magnitudes of the FFT bins are thesame for the real BLE long range signal compared to the used bins of thespoof signal. Although all 6 frequency bins are shown (i.e., −375 kHz,−250 kHz, −125 kHz, +125 kHz, +250 kHz, +375 kHz) over the relevantfrequency spectrum, either all of these or fewer, such as the middle 4frequency bins (i.e., −250 kHz, −125 kHz, +125 kHz, +250 kHz), may beutilized in alternate embodiments.

The BLE Long-Range preamble is 10 repetitions of the bit sequence00111100, which is modulated as a Gaussian Frequency Shift Keying (GFSK)symbol at a symbol rate of 1 million symbols per second (MSymbol/s) witha modulation index of 0.5 and a bandwidth-time (BT) product of 0.5. Thisis substantially the same BT product as a standard BLE signal. In thefrequency-domain, this BLE Long-Range preamble signal consists of 6tones at the ±125 kHz, ±250 kHz, ±375 kHz frequency locations. Thepreamble repetition helps to concentrate the spectral energy in a subsetof bins. The inventive concept hones in on this concentration ofspectral energy. The exemplary spectrum is for a frequency error of 0kHz, but the method is robust for frequency error. The effect of afrequency error is to shift the 6 occupied bins substantially equally.If the bins are spaced at 15.625 kHz, an error of 46.875 kHz would shiftthe entire pattern 3 bins to the right (i.e., the occupied bins wouldchange from 9, 17, 25, 41, 49, and 57 to 12, 20, 28, 44, 52, and 60).

Turning to FIG. 5, a graphical comparison of coherent and incoherentsummation of the FFT bins for a BLE Long Range preamble signal receivedby an exemplary I/Q receiver, such as the I/Q receiver 200 of FIG. 2, isindicated generally by the reference numeral 500. Here, the coherentsummation 510 has substantially the same peak correlated magnitudeoutput as the incoherent summation 520.

A timewise correlation of two signals can be related to themultiplication of their Fourier transforms through the convolutiontheorem. Thus, the correlation of the received I/Q sequence signal withthe ideal I/Q sequence may be obtained by multiplying the FFT of thereceived I/Q with the FFT of the ideal signal. As the ideal signalconsists of just 6 bins, one need only consider these bins in themultiplication for a given frequency error. The timewise correlationwill have strong peaks every 8 μs. With the FFT, this information iscontained in the phases of the 6 tones. Coherently combining the FFToutput with a phase relationship corresponding to a unique sampling timeproduces the desired result for a timewise correlation. Following thismethodology, the FFT could either be performed many times to test allstarting times, or the results of one FFT could be considered with thetone phases of a series of starting time candidates.

The present exemplary embodiment combines the squared magnitudes of theFFT bins. This may reduce the SNR of the resulting correlation, butgreatly simplifies the processing as all of the symbol time candidatesmay be considered simultaneously. Once a BLE Long-Range signal has beendetected, the symbol time can then be calculated from the phases of theFFT bins.

Coherent combination would enforce a particular phase relationship onthe tones. So, one would multiply the tones from the FFT by “idealtones” known from the transmitted sequence and then sum. Whereasincoherent combination involves summing the squares of the tones so thephase information is lost. Correlation would always involve amultiplication, but one could modify the method to work on the absolutevalues. Squaring is preferred because absolute values can be vulnerableto obscure FFT artefacts such as from ramping the signal.

A comparison of coherent and incoherent summation may be achieved bysumming the squares or the absolute values, but it is not limitedthereto. All of the frequency error candidates are then accounted for byconsidering different sets of summed bins, as offset by the frequencyerror.

Turning now to FIG. 6, a method of operating an I/Q receiver forfrequency error estimation and symbol synchronization in low-energylong-range communications is indicated generally by the referencenumeral 600. Here, an input block 610 receives I/Q valued data andpasses control to a function block 620. The block 620 down-samples thedata to 1 MHz and passes control to a function block 630. The block 630buffers 64 samples of the data and passes control to a function block640. The block 640 performs a 64-point FFT on the samples at least every8 μs into 64 FFT bins and passes control to a function block 650. Theblock 650 calculates a square of the absolute value for all FFT bins andpasses control to a function block 660. The block 660 sums sets of 4 (or6) bins over 27 combinations to cover all frequency errors and passescontrol to a decision block 670. The block 670 takes the maximalcombination and compares it to a threshold, looping control back toblock 640 if the threshold is not exceeded, but passing control on to afunction block 680 if the threshold is exceeded. The block 680, in turn,uses the FFT bin phases to extract Symbol timing.

Thus, the processing flow of the inventive concept operates on a bufferof I/Q data that has been down sampled to 1 MHz. 64 samples are storedin the buffer, which is 64 μs of signal while the total preamble lengthis 80 μs. Every 8 μs or less, an FFT is performed on this buffered data;the resulting output will be the real or in-phase and imaginary orquadrature-phase values of the 64 FFT bins. The sum of the absolutevalues squared of all of these bins is then taken. All bins are usedsince different frequency error candidates must typically be considered.The BLE specification allows for a transmitter to be in error by up to±150 kHz, while the receiver itself may have a frequency error of ±50kHz. Such large potential frequency errors must be accommodated becauseBluetooth™ was originally specified for relatively inexpensive hardwaredevices, and backward compatibility remains desirable.

Thus, frequency errors up to ±200 kHz are considered, and a 1.3 MHzfilter bandwidth suffices as being 300 kHz greater than the 1 MHzdown-sampled data rate. The bin spacing is 1 MHz/64=15.625 kHz, so thiscalls for considering bin offsets of 200/15.625=12.8 bins. As onlyinteger bins can be considered, this is ±13 bins. Note that the tonespacing (125 kHz) is a multiple of the bin spacing (8*15.625 kHz), whichallows for a simpler implementation since all of the bins can be shiftedby a fixed number depending upon the frequency offset.

Due to the ten 8 μs repetitions of the 00111100 8-bit pattern in thepreamble for BLE Long-Range, the signal energy is concentrated in 6tones at ±125 kHz, ±250 kHz, and ±375 kHz. Embodiments of the presentinventive concept may use all six of these tones, or alternately justthe center four (i.e., ±125 kHz and ±250 kHz) since the outer two (i.e.,±375 kHz) should be of relatively lower magnitude. For the 0 Hz offsetbin, the absolute values squared of the bins (17, 25, 41, 49) arecombined when using the central 4 of the 6 bins. Using the absolutevalues squared is one way of assuring non-negative results forcomplex-valued I/Q samples. For ease of explanation regardless of theoffset frequency error, the 6 bins resulting from the preamble signalmay be thought of as any set of 6 bins (out of 64 in this embodiment)that could be seen in a frequency-domain plot through a mask or rulerwith 6 equidistant holes spaced at 125 kHz intervals.

After the 27 candidates have been calculated, the largest candidate iscompared against a threshold. If the threshold is exceeded, Sync isdetected. The two outer bins are not used in this exemplary embodimentsince they contain only half the signal strength of the inner bins, andtheir inclusion may exacerbate the detection of false maximums, such asone 8 bins offset from the true frequency error, which due to thepresence of noise might have a slightly larger magnitude than that ofthe true frequency error. By removing the 2 outer bins, only 2 of the 4remaining bins overlap in this case as compared to 4 of the 6 originalbins.

Setting or adjusting the sync threshold requires care. At low powerswith low SNR, a fixed threshold may be used. As the signal powerincreases, the threshold should increase or false Sync can be detectedbefore the buffer contains 64 samples of preamble. This is done here bysumming the absolute values squared of the buffered samples to give asignal power (P) estimate, where the threshold is then set according tothe following relationship:

thresh=max(fixed_(threshold), grad_threshold*P−threshold_offset)   (Eqn.1)

In BLE Long-Range, spacing between preamble tones is coincidentallyfixed by the standard to 125 kHz apart. If a different FFT length wereused, the interval between samples might not be 8 μs but wouldpreferably be an integer number of bins apart. That is, FFT length anddown-sampling rate are linked.

Frequency offsets at a half bin spacing, for example, will reduce themagnitude of the candidates by about 3 dB. To avoid this, alternateFFT's may be performed with a ½ bin frequency offset. As the preamblelength is 10 repetitions and only 8 are used for the FFT in thisexemplary embodiment, one FFT will then have a frequency error of lessthan ¼ bin.

I/Q data is used because I/Q takes advantage of sine and cosine signalsbeing mathematically orthogonal to each other, and therefore separablewith minimal effort. With appropriate care, one signal can be modulatedwith a cosine wave and the other with a sine wave that is basically adelayed version of the cosine wave, where these two signals remainseparable at the receiver even though their frequency spectrums overlap.I/Q pairs are the real and imaginary components of the complex-valuedtransmitted baseband signal. “I/Q data” refers to the real or in-phase(I) and imaginary or quadrature-phase (Q) samples of the constellationfor the modulation type used. There may be various pairs of I/Q“samples” that occur during interim processing. Although a complex I/Qdata signal is used in the exemplary embodiments, it shall be understoodthat alternate embodiments may use different signals, such as multiplesignals that are separated in time, frequency, phase, and/or quadrature.

An FFT is performed on the received I/Q data using an appropriate samplerate, such as the symbol rate. This places substantially all of thesignal energy into just the 6 bins allowing a significant increase inSNR. By summing the energy in various candidate sets of the 6 bins, orof the inner 4 bins in some embodiments, it is possible at low SNR todetermine both the presence of a BLE Long-Range signal as well as itsfrequency error. The relative phases of the bins can then be used todetermine fractional symbol timing with respect to the FFT window. Thisinformation is sufficient to achieve symbol synchronization and begindemodulation of the main BLE Long-Range packet.

Exemplary embodiments of the inventive concept use an FFT per block ofsamples to achieve time and frequency synchronization. This exploits therelatively low complexity of FFTs while maintaining de-noising gain. Therelatively low complexity using FFTs is due to the reduced increase incomplexity as nlogn for sequences of length n, which is significantlyless than for other methods that increase as n². In an exemplaryembodiment, 64 samples of I/Q data are stored where each I/Q data sampleuses a 9-bit word length for I and a 9-bit word length for Q. Each FFTblock uses the n=64 I/Q data samples covering 8 repetitions of the 8-bitBLE preamble pattern 00111100. In alternate embodiments, a block mayinclude a different number n of I/Q data samples. For example, n=80could cover all 10 repetitions of the preamble.

The inventive concept may further use a combining scheme to make thedetection more robust to frequency offsets. This balances thedifficulties of frequency error estimation with signal detection. Bymagnitude combining the candidate bins, SNR may be somewhat sacrificedto allow the consideration of multiple frequency error and sampling timecandidates in a highly efficient manner. Nonetheless, the SNR remainssufficient to successfully detect BLE Long-Range packets with a very lowfalse detection rate.

Thus, embodiments of the inventive concept require less hardware toimplement than time-domain correlation schemes. Time-domain correlationgiven de-sensitization of the correlation by frequency error wouldrequire a large number of simultaneous correlations to be performed,such as 20 for example. Time-domain correlation might otherwise offerbetter performance at low SNR, but insufficient benefit would berealized since performance is limited by the bit error rate (BER) forboth Sync methodologies. It shall be understood that this is the BER ofthe access code and payload demodulation, even with ideal Sync.

The inventive concept has a substantially lower SNR threshold for asuccessful detection then frequency-domain correlation. In theory,frequency-domain correlation is simpler as it avoids an FFT, buthardware implementation is likely to be at least as expensive. As anexemplary embodiment of the present inventive concept can determinesymbol timing using the tone phases, it is only required every 8 μs. Forfrequency-domain correlation, the correlation would be determined farmore frequently such as per sample or faster than the 1 MSample/s in thebuffer since, there, the correlation peak or the like is used to derivethe symbol timing.

The method of the present inventive concept makes use of the energy inthe BLE Long-Range preamble being concentrated at 6 tones (i.e., −375kHz, −250 kHz, −125 kHz, +125 kHz, +250 kHz, +375 kHz). These have aspecific magnitude relationship (i.e., 0.47, 1, 0.91, −0.91, 1, −0.47)at sample offset 1=0. By adjusting the magnitude relationship, aspoofing signal waveform may be constructed that while it should bedetected by the FFT synchronization algorithm, should not cause eitherI/Q correlation or frequency-domain correlation to detectsynchronization. A possible candidate for this spoofing signal would be[0.5 1 0.9 −0.9 −1 −0.5]. This signal uses amplitude modulation (AM), soit would not be seen by a frequency synchronizer and thus the responseof an I/Q correlation should be substantially reduced.

The next step of the inventive concept is to extract the symbol timing.This can be done from the phases of the FFT bins. The phases of the FFTbins vary with starting time as outlined below. t=0 is exact alignmentwith the 00111100 * 8 pattern where t is the offset in input buffersamples from that alignment. t's range is 0 to 63, but as the FFT isrepeated at least every 8 μs, the correction is only needed over an 8sample (8 ps) range. The bin numbers (e.g., −8) are given relative tothe center bin. This center bin includes the offset for the selectedfrequency error candidate.

$\begin{matrix}{{{Y\left\lbrack {- 16} \right\rbrack} = {{- \frac{t}{2}}\pi}},\mspace{14mu} {{Y\left\lbrack {- 8} \right\rbrack} = {{- \frac{t}{4}}\pi}},\mspace{14mu} {{Y\lbrack 8\rbrack} = {\pi + {\frac{t}{4}\pi}}},{{Y\lbrack 16\rbrack} = {\frac{t}{2}\pi}}} & \left( {{Eqn}.\mspace{14mu} 2} \right)\end{matrix}$

The difference between Y[−16] and Y[16] might provide the greatestaccuracy, but will change through 8π in 8 samples providing an ambiguousanswer. The phase difference between any two pairs of bins where thebins of each pair are each separated by 8 bins can be used to resolvethe ambiguity. The phase difference between bins (−16 & −8) and (8 & 16)is used by calculating:

$\begin{matrix}{{{Coarse}\mspace{14mu} {Timing}} = {\frac{4}{\pi}{{angle}\left( {{{Y\left\lbrack {- 8} \right\rbrack}*\overset{\_}{Y\left\lbrack {- 16} \right\rbrack}} - {{Y\lbrack 16\rbrack}*\overset{\_}{Y\lbrack 8\rbrack}}} \right)}}} & \left( {{Eqn}.\mspace{14mu} 3} \right) \\{= {\frac{4}{\pi}\; {angle}\; \left( {{e^{{- j}\frac{t\; \pi}{4}} \times e^{j\frac{t\; \pi}{2}}} - {e^{j\frac{t\; \pi}{2\;}} \times e^{- {j{({\pi + \frac{t\; \pi}{4}})}}}}} \right)}} & \left( {{Eqn}.\mspace{14mu} 4} \right) \\{= {{\frac{4}{\pi}\; {angle}\; \left( {e^{j\frac{t\; \pi}{4}} + e^{j\frac{t\; \pi}{4}}} \right)} = {{\frac{4}{\pi}\; {{angle}\left( {2\; e^{j\frac{t\; \pi}{4}}} \right)}} = t}}} & \left( {{Eqn}.\mspace{14mu} 5} \right)\end{matrix}$

To get a high accuracy estimate for the symbol timing,

$\begin{matrix}{\theta = {\frac{1}{\pi}{angle}\; \left( {{Y\left\lbrack {- 16} \right\rbrack}*\overset{\_}{Y\left\lbrack {- 16} \right\rbrack}} \right)}} & \left( {{Eqn}.\mspace{14mu} 6} \right)\end{matrix}$

is used to derive 4 timing candidates of 0+θ, 2+θ, 4+0 and 6+θ. Theclosest candidate to the coarse timing will then recover the symboltiming. By retaining fractional accuracy, this gives an accurate symboltiming even with decimation to 1 MHz.

Fractional symbol timing may be determined based on relative frequencybin phases where the block transformation is an n-point time-domain tofrequency-domain transform. Here, the fractional symbol timing isdetermined in accordance with relative frequency bin phases of first andsecond bins separated by n/2 bins for determining high-precision symboltiming with an ambiguity, a third bin separated from the first bin byn/8 bins and a fourth bin separated from the second bin by n/8 bins forresolving the ambiguity. This bin spacing is applicable to BLE longrange with the given FFT length.

The inventive concept is not limited to the direct conversion receiverarchitecture illustrated, and could be applied to other receiverarchitectures such as super-heterodyne receivers or the like. The choiceof FFT length and buffering rate is arbitrary. Combinations which makethe tone spacing an integer multiple of the bin spacing will make theprocessing simpler since the frequency candidates are integer shifts,but with added complexity non-integer fractional shifts may beaccommodated.

It is also possible to sum the absolute values of the bins and comparethis to a threshold and to make use of the outer two bins. If using theouter bins for offsets larger than 7, then a circular shift(“circshift”) operation may be applied to any bins below 0 or above 63since the tone may alias. This is feasible since the filtering beforethe buffering should not be exactly 1 MHz, but wider (e.g., 1.3 MHz)with allowance for any frequency error.

There are numerous algorithm choices for setting the threshold.Additionally, there are numerous choices for establishing the samplingtime from the FFT bin phases using different combinations of the tones.

Accordingly, the present inventive concept reduces the complexity of thecorrelator to increasing as nlogn using a FFT per block of samples toachieve time and frequency synchronization, rather than increasing as n²as in each of the traditional Cartesian correlation and the traditionalfrequency-domain correlation. This facilitates a significant reductionin correlator complexity for large n. It shall be understood thatperforming a single FFT multiple times is still possible, versusperforming a block FFT fewer times.

Although exemplary embodiments of the present inventive concept havebeen shown and described, it shall be understood that those of ordinaryskill in the pertinent art may make changes therein without departingfrom the scope, principles, and spirit of the present inventive conceptas defined by the appended claims and their equivalents.

1. A method for symbol synchronization in a frequency-modulatedtransmission having a preamble, the method comprising: receiving thefrequency-modulated transmission and obtaining a sequence of time-domainsamples of the preamble; transforming the sequence of time-domainsamples into a spectrum of frequency-domain data over discretefrequencies arranged in a plurality of frequency bins; comparingcombined energies for each of a plurality of subsets of the frequencybins, each subset corresponding to a relative frequency distribution ofenergy expected in the preamble at a respective carrier frequency;selecting the subset of the frequency bins with the greatest combinedenergy, the selected subset being indicative of a carrier frequencyerror of the transmission; and synchronizing receipt of thefrequency-modulated transmission in accordance with the selected subsetof the frequency bins.
 2. The method of claim 1, wherein thesynchronizing receipt of the frequency-modulated transmission inaccordance with the selected subset of the frequency bins comprisescomparing phase relationships at the plurality of discrete frequenciesto determine symbol timing.
 3. The method of claim 1 wherein thefrequency-modulated transmission is a Guassian frequency-shift-keying(FSK) modulated transmission.
 4. The method of claim 1, wherein thereceiving of the frequency-modulated transmission comprises: receiving aplurality of periodic samples of the frequency-modulated transmission;buffering the plurality of the received periodic samples; and whereinthe transforming comprises: performing a block transformation on theplurality of buffered periodic samples into the plurality of frequencybins.
 5. The method of claim 4, further comprising comparing thecombined energies to a threshold, wherein if the combined energies doesnot exceed the threshold, receiving the next periodic samples, orwherein if the combined energies exceeds the threshold, synchronizingthe transmission and determining a fine carrier frequency error.
 6. Themethod of claim 1, further comprising determining fractional symboltiming based on relative frequency bin phases.
 7. The method of claim 4,wherein: the block transformation is an n-point time-domain tofrequency-domain transform, and fractional symbol timing is determinedin accordance with relative frequency bin phases of first and secondbins separated by n/2 bins for determining high-precision symbol timingwith an ambiguity, a third bin separated from the first bin by n/8 binsand a fourth bin separated from the second bin by n/8 bins for resolvingthe ambiguity.
 8. The method of claim 4, wherein the blocktransformation is a 64-point Fast Fourier Transform (FFT).
 9. The methodof claim 1, further comprising: achieving symbol timing synchronization;and beginning demodulation of a main packet based on the achieved symboltiming synchronization.
 10. The method of claim 4, further comprising:comparing the greatest combined energy of the subset to a threshold; andif the greatest combined energy exceeds the threshold, using frequencybin phases to extract symbol timing.
 11. The method of claim 1, whereinthe frequency-modulated transmission is a Bluetooth™ Low-EnergyLong-Range transmission, and the preamble includes ten 8 μs repetitionsof the 8-bit pattern
 00111100. 12. The method of claim 1 wherein thecarrier frequency error is based on a fractional bin spacing.
 13. Themethod of claim 1, further comprising performing an alternate FFT with a½ bin frequency offset to obtain a carrier frequency error within ¼ bin.14. A receiving apparatus for symbol synchronization in afrequency-modulated transmission having a preamble, the receivingapparatus comprising: a receiver configured to receive thefrequency-modulated transmission and obtain therefrom a sequence oftime-domain samples of the preamble; and a processor configured to:transform the sequence of time-domain samples into a spectrum offrequency-domain data over discrete frequencies arranged in a pluralityof frequency bins, compare combined energies for each of the pluralityof subsets of the frequency bins, each subset corresponding to arelative frequency distribution of energy expected in the preamble at arespective carrier frequency, select the subset of the frequency binswith the greatest combined energy, the selected subset being indicativeof a carrier frequency error of the transmission, and synchronizereceipt of the frequency-modulated transmission in accordance with theselected subset of the frequency bins.
 15. The receiving apparatus ofclaim 14, wherein the processor is further configured to compare phaserelationships at the plurality of discrete frequencies to determinesymbol timing.
 16. The receiving apparatus of claim 14, wherein thefrequency-modulated transmission is a Gaussian FSK modulatedtransmission.
 17. The receiving apparatus of claim 14, wherein: thereceiver is further configured to receive a plurality of periodicsamples of the frequency-modulated transmission; and the processor isfurther configured to: buffer the plurality of the received periodicsamples to a buffer, perform a block transformation on the plurality ofbuffered periodic samples into the plurality of frequency bins.
 18. Thereceiving apparatus of claim 17, wherein the processor is furtherconfigured to compare the combined energies to a threshold, wherein ifthe combined energies does not exceed the threshold, the processor isfurther configured to receive the next periodic samples, and wherein ifthe combined energies exceeds the threshold, the processor is furtherconfigured to synchronize the transmission, and determine a fine carrierfrequency error.
 19. The receiving apparatus of claim 14, wherein theprocessor further configured to determine fractional symbol timing basedon relative frequency bin phases.
 20. A program storage device tangiblyembodying a program of instruction steps executable by a processor forreceiver symbol synchronization in a frequency-modulated transmissionhaving a preamble, the instruction steps comprising: receiving thefrequency-modulated transmission and obtaining a sequence of timesamples of the preamble; transforming the sequence of time-domainsamples into a spectrum of frequency-domain data over discrete frequencyarranged in a plurality of frequency bins; comparing combined energiesfor each of a plurality of subsets of the frequency bins, each subsetcorresponding to a relative frequency distribution of energy expected inthe preamble at a respective carrier frequency; selective the subset ofthe frequency bins with the greatest combined energy, the selectedsubset being indicative of a carrier frequency error of thetransmission; and synchronizing receipt of the frequency-modulatedtransmission in accordance with the selected subset of the frequencybins.